Problem: As you very well know, this year's funkiest numbers are so called triangular numbers (that is, integers that are representable as <image>, where k is some positive integer), and the coolest numbers are those that are representable as a sum of two triangular numbers.

A well-known hipster Andrew adores everything funky and cool but unfortunately, he isn't good at maths. Given number n, help him define whether this number can be represented by a sum of two triangular numbers (not necessarily different)!

Input

The first input line contains an integer n (1 ≤ n ≤ 109).

Output

Print "YES" (without the quotes), if n can be represented as a sum of two triangular numbers, otherwise print "NO" (without the quotes).

Examples

Input

256


Output

YES


Input

512


Output

NO

Note

In the first sample number <image>.

In the second sample number 512 can not be represented as a sum of two triangular numbers.

Solution (in PYTHON):

Solution:
import math
n = int(raw_input())
end = (int(math.sqrt(n * 2)) + 10)
ans = 'NO'
i = 1
while i <= end and i <= n:
    a = i * (i + 1) / 2
    b = (n - a) * 2
    if b <= 0:
        print 'NO'
        break
    d = 1 + 4 * b
    sd = int(math.sqrt(d))
    if sd * sd == d:
        if (sd - 1) % 2 == 0:
            print 'YES'
            break
    i += 1
else:
    print 'NO'